Question

Find the area of the following design excluding the square region.

Answer 1

First write the lengths of sides of the one triangular shape of the design.
Then, find the semiperimeter “s” of the selected triangular part .
Next, find the area of the selected triangular part of the design.
Since, we know all three sides of the triangular part of the design, so use Heron’s formula to calculate its area.
Given, $a=25$ cm, $b=20$ cm, $c=25$ cm
So, the semi perimeter of the triangle is given as:
$s=\frac{a+b+c}{2}$
$\Rightarrow s=\frac{25+20+25}{2}=\frac{70}{2}=35$
Now, the area of the triangle
$A=\sqrt{s(s-a)(s-b)(s-c)}$
$\Rightarrow A=\sqrt{35(35-25)(35-20)(35-25)}$
$\Rightarrow A=\sqrt{35\times 10\times 15\times 10}$
$\Rightarrow A=50\sqrt{21}$
$\Rightarrow A=50\times 4.582$
$\Rightarrow A=229.1c{m}^2$